You could try submitting a enhancement request bug report for this Bluetooth audio capability, but it's very likely a dup, as it's been asked about in the forums here for years.
You are correct in that you cannot currently play out via A2DP while accepting input via HFP. There is a comment in the "Note" section of Q&A1799 "AVAudioSession - Microphone Selection" discussing HFP and AVAudioSessionCategoryPlayAndRecord with respect to the Input case. https://developer.apple.com/library/ios/qa/qa1799/_index.html
It is unfortunate that the document formatting is messed up in that the "Note" box doesn't actually surround all the relevant text, but here's the important bit:
"If an application uses the
setPreferredInput:error:method to select a Bluetooth HFP input, the output will automatically be changed to the Bluetooth HFP output. Moreover, selecting a Bluetooth HFP output using the
MPVolumeView's route picker will automatically change the input to the Bluetooth HFP input. Therefore both the input and output will always end up on the Bluetooth HFP device even though only the input or output was set individually."
The A2DP route is available to you in AVAudioSessionPlayback but will not be in AVAudioSessionCategoryPlayAndRecord.
Definitely file an enhancement request bug, doesn't matter if it's a duplicate - in fact, the more duplicates the better as this indicates the popularity of the requested feature.